Self-orthogonal codes with dual distance three and quantum codes with distance three over
$$\mathbb F _5$$
F
5

Self-orthogonal codes with dual distance three and quantum codes with distance three over...
Liang, Fangchi
2013-08-10 00:00:00
Self-orthogonal codes with dual distance three and quantum codes with distance three constructed from self-orthogonal codes over
$$\mathbb F _5$$
F
5
are discussed in this paper. Firstly, for given code length
$$n\ge 5$$
n
≥
5
, a
$$[n,k]_{5}$$
[
n
,
k
]
5
self-orthogonal code with minimal dimension
$$k$$
k
and dual distance three is constructed. Secondly, for each
$$n\ge 5$$
n
≥
5
, two nested self-orthogonal codes with dual distance two and three are constructed, and consequently quantum code of length
$$n$$
n
and distance three is constructed via Steane construction. All of these quantum codes constructed via Steane construction are optimal or near optimal according to the quantum Hamming bound.
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Self-orthogonal codes with dual distance three and quantum codes with distance three over
$$\mathbb F _5$$
F
5

Abstract

Self-orthogonal codes with dual distance three and quantum codes with distance three constructed from self-orthogonal codes over
$$\mathbb F _5$$
F
5
are discussed in this paper. Firstly, for given code length
$$n\ge 5$$
n
≥
5
, a
$$[n,k]_{5}$$
[
n
,
k
]
5
self-orthogonal code with minimal dimension
$$k$$
k
and dual distance three is constructed. Secondly, for each
$$n\ge 5$$
n
≥
5
, two nested self-orthogonal codes with dual distance two and three are constructed, and consequently quantum code of length
$$n$$
n
and distance three is constructed via Steane construction. All of these quantum codes constructed via Steane construction are optimal or near optimal according to the quantum Hamming bound.